c1s3 - 1 1.3 Matrices and Their Algebra Chapter 1 Vectors...

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1.3 Matrices and Their Algebra 1 Chapter 1. Vectors, Matrices, and Linear Spaces 1.3. Matrices and Their Algebra Defnition. A matrix is a rectangluar array of numbers. An m × n matrix is a matrix with m rows and n columns : A =[ a ij ]= a 11 a 12 ··· a 1 n a 21 a 22 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a mn . Defnition 1.8. Let A =[ a ik ]bean m × n matrix and let B =[ b kj ]be an n × s matrix. The matrix product AB is the m × s matrix C =[ c ij ] where c ij is the dot product of the i th row vector of A and the j th column vector of B : c ij = n k =1 a ik b kj .
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1.3 Matrices and Their Algebra 2 Note. We can draw a picture of this process as: Example. Page 46 number 16. Defnition. The main diagonal of an n × n matrix is the set { a 11 ,a 22 , ...,a nn } . A square matrix which has zeros oF the main diagonal is a diagonal matrix . We denote the n × n diagonal matrix with all diagonal
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This note was uploaded on 02/24/2012 for the course MATH 285 taught by Professor Igordolgachev during the Fall '04 term at University of Michigan-Dearborn.

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c1s3 - 1 1.3 Matrices and Their Algebra Chapter 1 Vectors...

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